\hspace{-16}$4 balls are to be selected from a group of 11 bolls. 5 of them are of type A,\\\\ 2 of them are type B, 2 are of type R, one of type K and one of type D.\\\\ Q.In how many ways we can arrange 4 balls out of these 11 balls in a line
http://www.askiitians.com/forums/Algebra/22/47891/permutation-and-combination.htm
11there are 5 cases.
case-1
all the 4 balls are same i.e. of type A
case-2
balls are of same type in pairs & there are 2 pairs
case-3
3 balls are of same type & one is different
case-4
two balls are of same type & another 2 r of different type
case-5
all the 4 balls are of different type
case-1+case-2+case-3+case-4=1+3C2(4!/2!.2!)+4.4!/3!+3.4C2.4!/2!+5P4
21Case 1:
choose 4 from A in 5C4 ways.
Case 2:
Choose 3 from A and any one from the rest.no of such ways..= (5C3X2C1)+(5C3X2C1)+(5C3X1)+(53X1)
Case 3 :
Choose 2 from A AND 2 From the rest.no of such ways..= (5C2X2c2)x2+(5c2X2c1)X2
CASE 4 :
Choose 1 from A and 3 from the rest..no of ways=5c1X2c2X2c1)X2+(5c1X2c2X1)X4
